Abstract:

The author proposed an iterative algorithm for complex linear equations of   symmetric positive definite sparse matrices based on GPU. First, the author used the conjugate gradient method and double conjugate gradient algorithm based on GPU to achieve  the operation of matrix vector multiplication, and  optimized the corresponding algorithm steps fully. Second, in order to realize the 3 pretreatment methods, which were  diagonal element preprocessing step based on GPU, incomplete Cholesky decomposition and symmetric super relaxation, the author proposed  a parallel algorithm for solving triangular systems based on GPU. Finally, the advantage and disadvantage of various pretreatment methods were analyzed through experiments. The experimental results show that the speed of the algorithm is higher than the  CPU serial iterative algorithm and the classical direct method, and the maximum speed is up to 76 times faster than that of two methods.

Key words: complex linear equation, iterative method, GPU computing